Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C61×#585 ⋊ C4 |
| Sylow | C61 ⋊ #62654 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×#6923 |
| commutator, socle | C2×C61 | C25×C4 |
| Fitting | C61×#585 | C4 |
| prime radical | #585×D61 | C2 |
| cosocle | C2×D61 | C26 |
| hypercenter | #585 | #6923 |
| hypocenter | C61 | #62654 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ #585 | |
11222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^8,61|a^2=h,f^2=g,b^a=bg,f^a=fg,i^a=i^11,e^b=eg,d^c=dg,i^h=i^60640 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1116289);